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Fun GCSE Maths: Circles, Angles, and Formulas!

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Aanya Patel

29/04/2023

Maths

GCSE Maths Higher Revision Formulas

Fun GCSE Maths: Circles, Angles, and Formulas!

This comprehensive guide covers essential topics for GCSE maths higher circle theorems revision, including trigonometry, probability, and quadratic equations. It provides key formulas, theorems, and problem-solving techniques for students preparing for their GCSE exams.

Key points:

  • Circle theorems and their applications
  • Trigonometry formulas and SOHCAHTOA
  • Probability concepts and calculations
  • Quadratic equations and the quadratic formula
  • Data analysis and graphing techniques
...

29/04/2023

14883

DIAMETER
RADIUS
RADIUS
ISOCELES A-
CIRCLE
THEOREMS
H
HGG
A
Opposite angies
in a cucric quad-
rilateral add up
to 180
Length
of two
Chord bis

View

Advanced Mathematical Concepts and Formulas

This page delves into more advanced mathematical concepts, building upon the foundations laid in the previous section. It covers a wide range of topics essential for GCSE maths higher circle theorems revision questions and other advanced mathematical problems.

The page begins with a discussion on graph transformations, explaining how different functions affect the shape and position of graphs.

Example: The function y = kfxx results in a vertical stretch or compression of the graph, depending on the value of k.

Various types of graphs are illustrated, including quadratic, cubic, and reciprocal functions. This visual representation helps students understand the characteristics of different mathematical functions.

The concept of sequences is introduced, with a focus on arithmetic and geometric progressions.

Formula: The nth term of an arithmetic sequence is given by a_n = a + n1n-1d, where a is the first term and d is the common difference.

The page also covers more advanced topics such as surds, loci, and the trapezoidal rule for approximating integrals.

Vocabulary: A surd is an expression involving square roots that cannot be simplified to remove the square root sign.

Financial mathematics is touched upon, with formulas for simple and compound interest provided.

Highlight: The compound interest formula is given as N = N₀1+r/1001 + r/100ⁿ, where N₀ is the principal amount, r is the interest rate, and n is the number of compounding periods.

The page concludes with additional geometric concepts, including the midpoint formula, gradient calculations, and the volume of frustrums.

Definition: A frustrum is the portion of a solid usuallyaconeorpyramidusually a cone or pyramid that lies between two parallel planes cutting the solid.

This comprehensive overview provides students with a solid foundation for tackling complex mathematical problems and excelling in their GCSE maths higher circle theorems revision.

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Maths

14,883

29 Apr 2023

2 pages

Fun GCSE Maths: Circles, Angles, and Formulas!

This comprehensive guide covers essential topics for GCSE maths higher circle theorems revision, including trigonometry, probability, and quadratic equations. It provides key formulas, theorems, and problem-solving techniques for students preparing for their GCSE exams.

Key points:

  • Circle theorems and... Show more

DIAMETER
RADIUS
RADIUS
ISOCELES A-
CIRCLE
THEOREMS
H
HGG
A
Opposite angies
in a cucric quad-
rilateral add up
to 180
Length
of two
Chord bis

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Join milions of students

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Advanced Mathematical Concepts and Formulas

This page delves into more advanced mathematical concepts, building upon the foundations laid in the previous section. It covers a wide range of topics essential for GCSE maths higher circle theorems revision questions and other advanced mathematical problems.

The page begins with a discussion on graph transformations, explaining how different functions affect the shape and position of graphs.

Example: The function y = kfxx results in a vertical stretch or compression of the graph, depending on the value of k.

Various types of graphs are illustrated, including quadratic, cubic, and reciprocal functions. This visual representation helps students understand the characteristics of different mathematical functions.

The concept of sequences is introduced, with a focus on arithmetic and geometric progressions.

Formula: The nth term of an arithmetic sequence is given by a_n = a + n1n-1d, where a is the first term and d is the common difference.

The page also covers more advanced topics such as surds, loci, and the trapezoidal rule for approximating integrals.

Vocabulary: A surd is an expression involving square roots that cannot be simplified to remove the square root sign.

Financial mathematics is touched upon, with formulas for simple and compound interest provided.

Highlight: The compound interest formula is given as N = N₀1+r/1001 + r/100ⁿ, where N₀ is the principal amount, r is the interest rate, and n is the number of compounding periods.

The page concludes with additional geometric concepts, including the midpoint formula, gradient calculations, and the volume of frustrums.

Definition: A frustrum is the portion of a solid usuallyaconeorpyramidusually a cone or pyramid that lies between two parallel planes cutting the solid.

This comprehensive overview provides students with a solid foundation for tackling complex mathematical problems and excelling in their GCSE maths higher circle theorems revision.

DIAMETER
RADIUS
RADIUS
ISOCELES A-
CIRCLE
THEOREMS
H
HGG
A
Opposite angies
in a cucric quad-
rilateral add up
to 180
Length
of two
Chord bis

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Circle Theorems and Trigonometry

This page covers essential concepts in geometry, focusing on circle theorems and trigonometry. It provides a comprehensive overview of key formulas and principles that are crucial for GCSE maths higher circle theorems revision.

The page begins with a detailed diagram illustrating various circle theorems. These theorems are fundamental to understanding the properties of circles and their applications in geometry problems.

Highlight: Circle theorems covered include angles in a cyclic quadrilateral, tangent-radius relationship, and angles in the same segment.

The page then transitions to trigonometry, introducing the SOHCAHTOA mnemonic for remembering trigonometric ratios.

Definition: SOHCAHTOA stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.

Additional trigonometric concepts are presented, including the sine and cosine rules for non-right-angled triangles.

Example: The sine rule is given as a/sinAa / sin A = b/sinBb / sin B = c/sinCc / sin C, while the cosine rule is expressed as a² = b² + c² - 2bc cos A.

The page also covers data analysis techniques, specifically focusing on cumulative frequency graphs and their interpretation.

Vocabulary: Interquartile range is defined as the distance between the 1st and 3rd quartiles on the bottom scale of a cumulative frequency graph.

Probability concepts are briefly mentioned, along with the quadratic formula for solving quadratic equations.

Formula: The quadratic formula is given as x = b±(b24ac-b ± √(b² - 4ac) / 2a for the equation ax² + bx + c = 0.

The page concludes with a collection of useful formulas for areas and volumes of various geometric shapes, including circles, polygons, and three-dimensional objects.

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Elisha

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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user